MEG and fMRI offer complementary insights into connected human brain function. Evidence from the use of both techniques in the study of networked activity indicates that functional connectivity reflects almost every measurable aspect of human reality, being indicative of ability and deteriorating with disease. Functional network analyses may offer improved prediction of dysfunction and characterisation of cognition. Three factors holding back progress are the difficulty in synthesising information from multiple imaging modalities; a need for accurate modelling of connectivity in individual subjects, not just average effects; and a lack of scalable solutions to these problems that are applicable in a big-data setting. I propose two methodological advances that tackle these issues. A confound to network analysis in MEG, the artificial correlations induced across the brain by the process of source reconstruction, prevents the transfer of connectivity models from fMRI to MEG. The first advance is a fast correction for this confound, allowing comparable analyses to be performed in both modalities. A comparative study demonstrates that this new approach for MEG shows better repeatability for connectivity estimation, both within and between subjects, than a wide range of alternative models in popular use. A case-study analysis uses both fMRI and MEG recordings from a large dataset to determine the genetic basis for functional connectivity in the human brain. Genes account for 20% - 65% of the variation in connectivity, and outweigh the influence of the developmental environment. The second advance is a Bayesian hierarchical model for sparse functional networks that is applicable to both modalities. By sharing information over a group of subjects, more accurate estimates can be constructed for individuals' connectivity patterns. The approach scales to large datasets, outperforms state-of-the-art methods, and can provide a 50% noise reduction in MEG resting-state networks.